The cost C, in thousands of dollars, of tuition for a year...

The cost $C,$ in thousands of dollars, of tuition for a year at a private four-year college can be approximated by $C=\frac{6}{5} t+14$ where $t$ is the number of years since $1995 .$ Graph the equation and use the graph to estimate the cost of tuition at a private four-year college in 2012 .

Key Concepts

Y-Intercept

The y-intercept in a linear equation is the constant term that represents the value of the dependent variable when the independent variable is zero. This concept provides a starting point for the line on a graph, which can be critical for interpreting data models and predictions.

Graphing Linear Equations

Graphing linear equations involves plotting the y-intercept on the vertical axis and using the slope to determine additional points along the line. This visual representation aids in understanding and analyzing the behavior and trends of the relationship between the variables.

Linear Functions

A linear function represents a relationship between two variables with a constant rate of change. It is typically expressed in the form y = mx + b, indicating a straight line when graphed. This concept is fundamental in understanding proportional, additive relationships in various fields of study.

Slope

The slope of a linear function is the coefficient that describes the rate at which the dependent variable changes with respect to the independent variable. It indicates the steepness and direction of the line, which is essential in delineating how quickly one quantity increases or decreases relative to another.

Function Evaluation

Function evaluation is the process of substituting a specific value for the independent variable into a function to determine the corresponding output. This skill is crucial for making predictions and estimating values in various mathematical and real-world contexts.

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